Not necessarily, but if they invite you for dinner you may bring something, anything is ok, Chinese people know that you are not really aware of their traditions... its better to ask your host if you should bring something or not...

Do like everyone else: give something you were given. Circle the presents!

Gifts go a long way here. I usually give gifts to those who have helped or been extra nice to me all year. This is not a long list so the wallet doesn't take a beating. For example, the girl that heads the Foreign Language Department at work is tops on my list. She's not a great friend or anything like that but I do search out a bottle of Canadian Ice Wine for her. When the time arises and I need a favor like a few extra vacation days or help with scheduling, she obliges, usually.

According to Chinese tradition and customs, on New Lunar Year Day, you do not do any work at home, and spend the day visiting family and friends.  If you do that, one of the common gifts is a basket or a box of fruits.  If you do not visit, no need to give presents then.

In general, red envelopes are only given to children of family members and close friends.  Maybe those under teenager years, and not ,married yet.  Amount inside red envelope varies according to age, with those in the 16 to 18 years old get 100 Rmb tops, maybe down to 10 to 25 Rmb bracket for the real younger ones.

Those are the gift situations I have experienced here at Spring Festival.   It doesn't mean either to be taken as a rigid rule, if someone has been nice to you, it will be a good time to say "Hello", wish good fortune and health, and hand out a present.  Please remember, in China it isn not the cost of the present, but the thought of buying a present for a special person.